A　matrix　is　called　a　lattice　matrix　if　its　elements　belong　to　a　distributive　lattice.　For　a　lattice　matrix　A　of　order　n,　if　there　exists　an　n　×　n　permutation　matrix　P　such　that　F　=　PAPT　=　(fij)　satisfies　fij　fji　for　i　＞　j,　then　F　is　called　a　canonical　form　of　A.　In　this　paper,　the　transitivity　of　powers　and　the　transitive　closure　of　a　lattice　matrix　are　studied,　and　the　convergence　of　powers　of　transitive　lattice　matrices　is　considered.　Also,　the　problem　of　the　canonical　form　of　a　transitive　lattice　matrix　is　further　discussed.　©　2004　Elsevier　Inc.　All　rights　reserved.